A game for two or more players in which one player makes a circle with his/her hand (sort of like an "OK" sign, or similar to the American Sign Language letter F) below their waist and attempts to get the other player(s) to look at it. If at least one other player looks at the person's hand in while it's making this sign below the waist, the person who got the others to look at their hand gets to punch all of the players who saw the circle, generally in the arm/shoulder area. This is generally a game that's played all day and out of the blue. The idea is to catch the other player(s) off guard and get them to look at the "circle" below your waist to get the privilege of punching them.

Player 1 and Player 2 are good friends and know that the Circle Game is always in play.

Player 1: "Hey dude, check out this bruise on my knee."
*Player 2 looks down at Player 1's knee, and sees that Player 1 has made the Circle sign below his waist*
*Player 1 punches Player 2*

as played in Malcolm in the Middle episode dinner out in season 2, it's a game where you have to avoid looking down and seeing someone with his/her hand in a circle below their waste. The opponent tries to trick you by saying something like "look a dollar" or is that your wallet down there" etc. If you do look at the hand formation of a circle, the person that tricked you gets to hit you in the arm as hard as he/she could.

The game is actually called "Balls" but is commonly refereed to as the circle game. It is called balls because the original objective of the game was to get someone to look at your balls. To play , you create a circle with your thumb and index finger ( like the ASL sign for the letter F) and you place it somewhere below your waist, preferably closer to your balls. Then you try to get someone to look at the circle. If they look at the circle, you get to say, "Hey man, why are you looking at my balls?" and punch them. But they do have a chance to not get punched. If they can put their finger in the circle and pull it back out before you close the circle on their finger, they don't get punched. If you do catch their finger, you get to say " Hey man, why are you trying to touch my balls?" and you punch them twice.
The game has no time limit and can even be played over the span of your life. kind of like the Slug Bug Game

The Circle Game has changed in the last 10-15yrs because the early players of it decided to add the complication of being "below the waist" so as to suggest they weren't actually got. OR to make it crude and a way to get someone to look in their genital region. The original game was simply a "Made you Look" concept with the only true rule being the circle couldn't be on your face or in the other persons direct face making it impossible not to actually look.

Official Rules - Old School
1) Make a circle with your thumb and pointer finger. It can be ANYWHERE, as long as its not on your face, or directly in the face of your opponent.
2) Try to make them look, this can be done any number of ways. The standard "Omg, what is this?" is always a winner.
3) Original rules said you got to do a bicep punch on the person, eventually that was moved to the shoulder - and inevitably it actually simply went away all together and became a simple "Got you" - which in itself for most game players was a win.
4) The circle can be broken as per variants of the game to reverse the punishment.

Some variants of the game include a "Couples" version. Where if either couple make a circle and their target looks at it, they are given owed a kiss. Breaking the circle reverses the winner. A silly game for young sweethearts but it can be flirty and playful.